1. Field of the Invention
The present invention is directed to a method for constructing a transversal gradient coil of the type employed in a nuclear magnetic resonance tomography apparatus.
2. Description of the Prior Art
As is known, a topical resolution of the nuclear magnetic resonance signals in a magnetic resonance tomography apparatus ensues by superimposing a magnetic field gradient on a uniform, static basic field on the order of magnitude of 1 T. The principles of such imaging are explained, for example, in the article "NMR Imaging Techniques and Applications: A Review", Bottomley, Review of Scientific Instrumentation, Vol. 53, No. 9, September 1982, pages 1319-1337. For obtaining a topical resolution in three dimensions, magnetic field gradients in three directions, preferably disposed perpendicularly relative to each other, must be generated. Conventional arrangements of transversal and axial gradient coils in a magnetic resonance imaging apparatus are shown in FIGS. 1 and 2, wherein a Cartesian coordinate system with axes respectively extending in the x, y, z directions is schematically shown to illustrate the directions of the respective gradients.
The conventional arrangement of transversal gradient coils shown in FIG. 1 is for generating a magnetic field gradient G.sub.y in y-direction. The gradient coils 2 are in the form of saddle coils, which are secured on a carrying cylinder 1. A substantially constant magnetic field gradient G.sub.y is generated in y-direction within a spherical examination volume 11 as a result of the conductor sections 2a. Due to their size and distance from the examination volume, the return conductors generate only slight magnetic field components in the examination volume 11, and these slight contributions are thus usually not considered in the design of the gradient coil.
The gradient coils for the generating the magnetic field gradient g.sub.x in the x-direction are constructed identical to the gradient coils 2 for the G.sub.y magnetic field gradient, but are rotated 90.degree. in azimuthal direction on the carrying cylinder 1. For clarity, the coils for generating the G.sub.x gradient are not shown in FIG. 1.
Axial gradient coils 3 for generating a magnetic field gradient G.sub.z in the z-direction are schematically shown in FIG. 2. The coils 3 are annular and are symmetrically disposed relative to the center of the examination volume 11. Because the two individual coils 3a and 3b have current flowing through them in opposite directions, as indicated in FIG. 2, they generate a magnetic field in the z-direction.
High demands are made on the linearity of the gradient fields in order to avoid image distortions. These high demands cannot be satisfied with the simple, schematically illustrated conductor structures shown in FIGS. 1 and 2. In particular, the transversal gradient coils for respectively generating the G.sub.x and G.sub.y gradients are complex in terms of design, and are the subject of the gradient coil construction method disclosed herein.
There are basically two procedures for designing gradient coils, namely the analytical projection method and the numerical projection method.
The analytical projection method inherently has the problem that the desired, linear field path, in its strictly mathematical form, results in solutions which cannot be technologically achieved, making the introduction of "relaxing" or "forgiving" boundary conditions necessary. Arbitrary error terms are attached to the algorithm with respect to degree, order and amplitude, which generally do not represent an optimum with respect to structures which can be physically or technologically achieved.
The numerical projection technique has the advantage that, on the basis of suitable mathematical organization methods (for example, least squares fit in the simplest case), deviations which are minimized only in their amplitude, but not with respect to the degree and to the order of the disturbance, are derived in addition to the desired field course. Because the projection already takes the physical nature of the arrangement into consideration, a "natural error spectrum" will be derived.
Due to the large parameter space, however, numerical methods are generally limited to simple coil geometries (for example, saddle coils).
A more complex coil geometry is disclosed in U.S. Pat. No. 4,456,881. The coil area is therein is subdivided into a plurality of surface elements. A current density vector is defined in each of these elements such that the current density distribution resulting therefrom generates the desired target field with a maximally permissible error amplitude. Because this method does not take the continuity condition into consideration, the coils calculated in this manner lack respective conductor returns. These are therefore attached to the outermost end of the coil, without taking their influence on the gradient field into consideration. A field error results therefrom, which constitutes a disadvantage of this known method.